# A Heuristic Charging Cost Optimization Algorithm for Residential Charging of Electric Vehicles

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## Abstract

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## 1. Introduction

_{2}emission from petroleum, natural gas, coal, geothermal, and automobile industries due to internal combustion engines (ICEs) automobiles discharging unhealthy CO

_{2}. Cars and trucks emit almost 26%, while other transportation methods account for about 12% of carbon dioxide emissions [1]. In the USA, transportation is the second-largest source (34%) of CO

_{2}emission, where light-duty vehicles (passenger cars and light trucks) and medium- and heavy-duty vehicles are responsible for almost 60% and 23%, respectively [2]. In 2019 about 1817 MMT emission of CO

_{2}from the transportation sector was recorded by the US department of energy [3]. Besides, the transportation sector is heavily dependent on the use of fossil fuels. Consequently, the automobile industry is rapidly moving towards electrified transportation, reducing CO

_{2}and dependencies on fossil fuels. Electric vehicles (EVs) possess numerous potential advantages over traditional vehicles, such as being environment friendly, the low cost of fuel, safety, being reliable, compact, and lightweight [4]. The EVs can be used as a distributed storage and could support power grid and microgrids, especially during peak demand through vehicle-to-grid (V2G) technology [5]. However, a large-scale penetration of EVs overloads the power grid with additional power demand, which may cause overloading of the transformer, feeder congestion, circuit faults, and instability in the overall grid operation [6]. The additional power demand requires the installation of new power generating sources and upgrading the existing power grid. However, this is not a feasible option, due to the high generation and infrastructure upgrade cost. A more feasible option is to shift the charging load from on-peak to off-peak time, assuming that the EVs are plugged in for charging in the evening after arrival at home [7]. This case takes advantage of the electricity tariff system and the dwell time of EVs to shift the charging load from on-peak to off-peak times and thereby respecting the grid operational boundaries. The utility companies provide different tariff systems with peak, mid-peak, and off-peak rates for customer convenience. These tariff systems provide fixed prices for specific times known as a time-of-use (TOU) tariff system. EV owners have the choice to either charge their EVs with or without fixed rate tariff systems. However, due to the uncertain nature of EV owners, it is difficult for them to follow the fixed TOU system. Besides, due to the fixed prices, the EVs herd toward the off-peak period, which results in overloading the grid [8]. Therefore, compared to the TOU system, the real-time prices (i.e., often update every 15 min) are more economical for grid operators and EV owners [9]. However, the charging control algorithm requires inputs, such as driving habits (i.e., arrival and departure time), battery characteristics (i.e., battery capacity and state-of-charge (SoC), and electricity market price using a communication network [10,11].

- We developed a charging cost optimization algorithm that learns the characteristics of EVs and real-time price patterns and computes a threshold value of price for each arrival and departure sequence of EVs. The threshold value is utilized to schedule the charging operation of EVs with minimizing the charging cost and respecting the operational constraints of the power grid.
- We show how the different schemes influence the charging cost and grid overloading by developing charging scenarios for individual and aggregated EVs with fixed and random arrival and departure sequences against the real-time electricity price patterns.
- We evaluated the performance of the proposed CCOA against the uncoordinated, flat-rate, and time-of-use systems in terms of charging cost and grid overloading.

## 2. Literature Survey

## 3. Proposed Charging Cost Optimization Algorithm

#### 3.1. Uncoordinated Charging

#### 3.2. Coordinated Charging

#### 3.2.1. Time-of-Use Tariff Systems

#### 3.2.2. The Proposed Charging Cost Optimization Algorithm

Algorithm 1 Main Algorithm of the proposed charging cost optimization algorithm (CCOA) | |

Input: Arrival and departure times, battery capacity, state-of-charge, and price profile
| |

Output: Optimal charging cost and electric load profiles
| |

1: Initialize the system local and global variables | |

2: Load the electric load (L) and price (P) vectors | |

3: for $t\leftarrow 1$ to $\left|T\right|$ do | |

4: for $i\leftarrow 1$ to $\left|N\right|$ do | |

5: Compute ${S}_{t}$ and ${E}^{r}$ | ▹ According to Equations (2) and (3) |

6: Compute $RT$ and ${P}_{h}$ | ▹ According to Equations (4) and (5) |

7: Validate constraint defined in Equation (9) | |

8: for $j\leftarrow 1$ to $\left|P\right|$ do | |

9: if ($P\left[j\right]$≤${P}_{h}\left[i\right]$) then | ▹ Validate constraint defined in Equation (8) |

10: $FTS\left[i\right]\leftarrow P\left[j\right]$ | ▹ Feasible time steps for charging |

11: end if | |

12: $j\leftarrow j+1$ | |

13: end for | |

14: end for | |

15: $temp\leftarrow FTS\left[1\right]$ | |

16: for $i\leftarrow 1$ to $\left|N\right|$ do | |

17: for $k\leftarrow 2$ to $\left|FTS\right|$ do | |

18: while ($l\le \left|RT\right[i\left]\right|$) do | |

19: if ($FTS\left[k\right]\le temp$) then | |

20: $OTS\left[l\right]\leftarrow FTS\left[k\right]$ | ▹ Optimal time steps with lowest cost |

21: $D\left[i\right]\leftarrow 1$ | |

22: $temp\leftarrow FTS\left[k\right]$ | |

23: end if | |

24: $l\leftarrow l+1$ | |

25: end while | |

26: end for | |

27: Charge_Control($N\left[i\right],OTS\left[l\right],RT\left[i\right],SoC\left[i\right],BC\left[i\right],{E}^{r}\left[i\right],D\left[i\right],P,L$) | |

28: Print the updated results | |

29: end for | |

30: $t\leftarrow t+1$ | |

31: end for |

- Step 1.
- Initialize all the system local and global variables (i.e., N, t, $i,j,k$, and the arrays) and load L and price P vectors.
- Step 2.
- Step 3.
- Collect the FTS for charging each of the i-th EVs according the threshold price value defined within their arrival and departure sequence in lines 7 to 12.
- Step 4.
- Get the first price value from the feasible time steps FTS a.k.a. the feasible solution set and compute the OTS by setting the decision D variable for each of the i-th EV in lines 15 to 25.
- Step 5.
- Call the subroutine Charge_Control (i.e., Algorithm 2). First, it validates constraints defined by Equations (10) and (11). Then, it checks the optimal charging steps, the decision variable, and the energy requirements and thereby controls the charging process of EVs according to their optimal schedules. For each charging, the activity updates the charging cost and the electric load vectors in lines 6 to 12. Finally, it returns the updated SoC, charging cost C, and electric load L vectors to Algorithm 1.
- Step 6.
- Print the updated results. Increment the time step t and repeat the process for the remaining intervals.

Algorithm 2 Charge_Control($N\left[i\right],OTS\left[l\right],RT\left[i\right],SoC\left[i\right],BC\left[i\right],{E}^{r}\left[i\right],D\left[i\right],P,L$) | |

1: Initialize local variables | |

2: for $j\leftarrow 1$ to $\left|P\right|$ do | |

3: while ($l\le \left|RT\right[i\left]\right|$) do | |

4: Validate constraint defined in Equations (10) and (11) | |

5: if ($(P\left[j\right]==OTS\left[l\right]\phantom{\rule{0.277778em}{0ex}}||\phantom{\rule{0.277778em}{0ex}}D\left[i\right]==1)\phantom{\rule{0.277778em}{0ex}}\&\&\phantom{\rule{0.277778em}{0ex}}SoC\left[i\right]\le {E}^{r}\left[i\right]$) then | |

6: $(SoC\left[i\right]\times BC\left[i\right])\leftarrow (SoC\left[i\right]\times BC\left[i\right])+(\eta \times {C}_{r})$ | ▹ Charge i-th EV |

7: $C\left[l\right]\leftarrow C\left[l\right]+C[l+1]$ | ▹ Update charging cost |

8: $L\left[l\right]\leftarrow L\left[l\right]+\left(SoC\right[i]\times BC[i\left]\right)$ | ▹ Update electric load |

9: else | |

10: $SoC\left[i\right]\leftarrow SoC[i-1]$ | |

11: $C\left[l\right]\leftarrow C\left[l\right]$ | |

12: $L\left[l\right]\leftarrow L\left[l\right]$ | |

13: end if | |

14: $l\leftarrow l+1$ | |

15: end while | |

16: end for | |

17: Return updated ($SoC\left[i\right]$, $C\left[l\right]$, and $L\left[l\right]$) |

## 4. Simulation Results and Discussion

#### 4.1. Individual Charging Scenario

#### 4.2. Aggregated Charging Scenario

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

EVs | electric vehicles |

CCOA | charging cost optimization algorithms |

CO_{2} | carbon dioxide |

ICEs | internal combustion engines |

MMT | million metric ton |

V2G | vehicle-to-grid |

TOU | time of use |

SoC | state-of-charge |

SoC_{min} | minimum state-of-charge |

SoC_{max} | maximum state-of-charge |

GA | genetic algorithm |

NHTS | National Household Travel Survey |

PEVs | plug-in electric vehicles |

MILP | mixed integer linear programming |

CSs | charging stations |

t | time step |

BC | battery capacity |

C | charging cost |

i | index of an EV |

E | energy |

P | charging price |

t_{a} | arrival time |

t_{d} | departure time |

S^{t} | stay time |

D | decision control variable |

kWh | kilowatt-hour |

P1 | off-peak/valley price |

P2 | mid-peak price price |

P3 | on-peak price price |

TSO | transmission system operator |

DSO | distribution system operator |

LV | low-voltage |

E_{r} | required amount of energy |

BC | battery capacity |

C_{r} | charging rate |

${C}_{r}^{min}$ | minimum charging rate |

${C}_{r}^{max}$ | maximum charging rate |

RT | required time to charge |

P_{h} | threshold price value |

L | electric load |

N | number of EVs array/vector |

T | maximum number of simulation steps |

i, j, k | loop control variables |

FTS | feasible time steps array/vector |

OTS | optimal time steps array/vector |

UCC | uncoordinated charging |

CFR | coordinated charging based on flat-rate |

CTOU | coordinated charging based on time-of-use |

V | voltage |

I | current |

μ | mean |

σ | standard deviation |

η | charging efficiency |

probability distribution function |

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**Figure 2.**Illustration of charging process and the cost. (

**a**). Standard tariff with flat rate (

**b**). Different time-of-use (TOU) tariff systems.

**Figure 6.**Battery charging process with uncontrolled charging (UCC), coordinated charging based on flat-rate (CFR), coordinated charging based on time-of-use (CTOU), and charging cost optimization algorithm (CCOA).

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## Share and Cite

**MDPI and ACS Style**

Hussain, S.; Thakur, S.; Shukla, S.; Breslin, J.G.; Jan, Q.; Khan, F.; Ahmad, I.; Marzband, M.; Madden, M.G. A Heuristic Charging Cost Optimization Algorithm for Residential Charging of Electric Vehicles. *Energies* **2022**, *15*, 1304.
https://doi.org/10.3390/en15041304

**AMA Style**

Hussain S, Thakur S, Shukla S, Breslin JG, Jan Q, Khan F, Ahmad I, Marzband M, Madden MG. A Heuristic Charging Cost Optimization Algorithm for Residential Charging of Electric Vehicles. *Energies*. 2022; 15(4):1304.
https://doi.org/10.3390/en15041304

**Chicago/Turabian Style**

Hussain, Shahid, Subhasis Thakur, Saurabh Shukla, John G. Breslin, Qasim Jan, Faisal Khan, Ibrar Ahmad, Mousa Marzband, and Michael G. Madden. 2022. "A Heuristic Charging Cost Optimization Algorithm for Residential Charging of Electric Vehicles" *Energies* 15, no. 4: 1304.
https://doi.org/10.3390/en15041304